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When we were balancing the Fe and Cu (Cathode and Anode, respectively) equations in the Hess's Law method in order to find the Ecell, why did we flip the Cu instead of the Fe equation? I know that we would get the same number but negative, but why is that a wrong answer and how are we supposed to know which equation to flip?
The E cell is the reduction potential plus the oxidation potential but the tables give only the reduction potentials. To get the oxidation potential you flip the reduction potential. Since the anode is being oxidized you flip that value since the given potential of the anode is the reduction potential of that reaction.
When calculating the Ecell, you know that you must always flip the value with a smaller voltage, as the Ecell must be positive since cells / batteries do work. The Cu has a smaller E value so when calculating the Ecell, the E value of Cu is "flipped".
You flip the oxidation reaction. The reason Ecell is supposed to be positive is that is has an inverse relationship with delta G so when it is positive delta G is negative and the reaction is spontaneous, when it is negative delta G is positive and the reverse reaction is spontaneous.
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